12/10/2012

Probability Generating Functions

• Suppose that the R.V. X can take on values in the set of nonnegative integers {0, 1, … }.  The probability generating function (p.g.f.) for X is g(t)=E[t^X].
• Examples
  • Find the p.g.f. for a R.V. that records the results of the flip of a balanced coin.
  • Use the p.g.f. to find the probability distribution of a R.V. that records the number of heads in four flips of a fair coin.
  • Use the p.g.f. to find the probability distribution for the number of spots on the upward facing sides of 8 dice.